Representation of an $\mathcal{H}^2$ -matrix. More...

Data Structures
struct	_h2matrix
	Representation of $\mathcal{H}^2$ -matrices. More...

struct	_h2matrixlist
	List of h2matrix objects. More...

Typedefs
typedef struct _h2matrix	h2matrix
	Representation of an $\mathcal{H}^2$ -matrix.

typedef h2matrix *	ph2matrix
	Pointer to h2matrix object.

typedef const h2matrix *	pch2matrix
	Pointer to constant h2matrix object.

typedef struct _h2matrixlist	h2matrixlist
	List of h2matrix objects.

typedef h2matrixlist *	ph2matrixlist
	Pointer to h2matrixlist object.

typedef const h2matrixlist *	pch2matrixlist
	Pointer to constant h2matrixlist object.

typedef void(*	h2matrix_callback_t) (ph2matrix G, uint mname, uint rname, uint cname, uint pardepth, void *data)
	Callback function for h2matrix iterators. More...

typedef void(*	h2matrixlist_callback_t) (pccluster t, uint tname, uint pardepth, pch2matrixlist hl, void *data)
	Callback function for h2matrixlist iterators. More...

Functions
ph2matrix	new_h2matrix (pclusterbasis rb, pclusterbasis cb)
	Create a new h2matrix object. More...

ph2matrix	new_uniform_h2matrix (pclusterbasis rb, pclusterbasis cb)
	Create a new h2matrix object representing a uniform matrix. More...

ph2matrix	new_full_h2matrix (pclusterbasis rb, pclusterbasis cb)
	Create a new h2matrix object representing a standard dense matrix. More...

ph2matrix	new_super_h2matrix (pclusterbasis rb, pclusterbasis cb, uint rsons, uint csons)
	Create a new hmatrix object representing a subdivided matrix. More...

ph2matrix	new_zero_h2matrix (pclusterbasis rb, pclusterbasis cb)
	Create a new h2matrix object representing a zero matrix. More...

ph2matrix	clonestructure_h2matrix (pch2matrix h2, pclusterbasis rb, pclusterbasis cb)
	Builds a new h2matrix with clusterbasis `rb` and `cb` and the block structure of `h2`. More...

ph2matrix	clone_h2matrix (pch2matrix h2, pclusterbasis rb, pclusterbasis cb)
	Builds a new h2matrix with clusterbasis `rb` and `cb` and the block structure of `h2`. Copies all coupling matrices $S_b,\ b \in \mathcal L_{\mathcal I \times \mathcal J}^+$ to the clone. More...

void	update_h2matrix (ph2matrix h2)
	Complete the initialisation of a h2matrix object. More...

void	del_h2matrix (ph2matrix h2)
	Delete an h2matrix object. More...

void	ref_h2matrix (ph2matrix *ptr, ph2matrix h2)
	Set a pointer to an h2matrix object, increase its reference counter, and decrease reference counter of original pointer target. More...

void	unref_h2matrix (ph2matrix h2)
	Reduce the reference counter of an h2matrix object. More...

size_t	getsize_h2matrix (pch2matrix h2)
	Get size of a given h2matrix object. More...

size_t	gettotalsize_h2matrix (pch2matrix h2)
	Get total size of a given h2matrix object, including cluster bases. More...

size_t	getnearsize_h2matrix (pch2matrix h2)
	Get size of the nearfield part of a given h2matrix object. More...

size_t	getfarsize_h2matrix (pch2matrix h2)
	Get size of the farfield part of a given h2matrix object. More...

void	clear_h2matrix (ph2matrix h2)
	Set an h2matrix to zero by clearing all far- and nearfield matrices. More...

void	scale_h2matrix (field alpha, ph2matrix h2)
	Scale an h2matrix by a factor. More...

void	random_h2matrix (ph2matrix h2)
	Fill an h2matrix with random coefficients. More...

ph2matrix	build_from_block_h2matrix (pcblock b, pclusterbasis rb, pclusterbasis cb)
	Build an h2matrix object from a block tree using given cluster bases. More...

pblock	build_from_h2matrix_block (pch2matrix G)
	Build an block tree from an h2matrix. More...

ph2matrix *	enumerate_h2matrix (ph2matrix h2)
	Enumerate h2matrix according to block tree. More...

void	iterate_h2matrix (ph2matrix G, uint mname, uint rname, uint cname, uint pardepth, h2matrix_callback_t pre, h2matrix_callback_t post, void *data)
	Iterate through all submatrices of an h2matrix. More...

void	iterate_rowlist_h2matrix (ph2matrix G, uint mname, uint rname, uint cname, uint pardepth, h2matrixlist_callback_t pre, h2matrixlist_callback_t post, void *data)
	Iterate through all submatrices of an h2matrix, collecting all row blocks in an h2matrixlist object. More...

void	iterate_collist_h2matrix (ph2matrix G, uint mname, uint rname, uint cname, uint pardepth, h2matrixlist_callback_t pre, h2matrixlist_callback_t post, void *data)
	Iterate through all submatrices of an h2matrix, collecting all column blocks in an h2matrixlist object. More...

void	iterate_byrow_h2matrix (ph2matrix G, uint mname, uint rname, uint cname, uint pardepth, h2matrix_callback_t pre, h2matrix_callback_t post, void *data)
	Iterate through all submatrices of an h2matrix. More...

void	iterate_bycol_h2matrix (ph2matrix G, uint mname, uint rname, uint cname, uint pardepth, h2matrix_callback_t pre, h2matrix_callback_t post, void *data)
	Iterate through all submatrices of an h2matrix. More...

void	mvm_h2matrix_avector (field alpha, bool h2trans, pch2matrix h2, pcavector x, pavector y)
	Matrix-vector multiplication $y \gets y + \alpha A x$ or $y \gets y + \alpha A^* x$ . More...

void	fastaddeval_h2matrix_avector (field alpha, pch2matrix h2, pavector xt, pavector yt)
	Interaction phase of the matrix-vector multiplication. More...

void	addeval_h2matrix_avector (field alpha, pch2matrix h2, pcavector x, pavector y)
	Matrix-vector multiplication $y \gets y + \alpha A x$ . More...

void	fastaddevaltrans_h2matrix_avector (field alpha, pch2matrix h2, pavector xt, pavector yt)
	Interaction phase of the adjoint matrix-vector multiplication. More...

void	addevaltrans_h2matrix_avector (field alpha, pch2matrix h2, pcavector x, pavector y)
	Adjoint matrix-vector multiplication $y \gets y + \alpha A^* x$ . More...

void	addevalsymm_h2matrix_avector (field alpha, pch2matrix h2, pcavector x, pavector y)
	Symmetric matrix-vector multiplication, $y \gets y + \alpha A x$ , where is assumed to be self-adjoint and only its lower triangular part is used. More...

void	fastaddmul_h2matrix_amatrix_amatrix (field alpha, bool atrans, pch2matrix A, pcamatrix Bt, pamatrix Ct)
	Interaction phase of the h2matrix - amatrix multiplication. More...

void	addmul_h2matrix_amatrix_amatrix (field alpha, bool atrans, pch2matrix A, bool btrans, pcamatrix B, pamatrix C)
	Matrix multiplication $C \gets C + \alpha A B$ , $C \gets C + \alpha A^* B$ , $C \gets C + \alpha A B^$ or $C \gets C + \alpha A^ B^*$ . More...

void	addmul_amatrix_h2matrix_amatrix (field alpha, bool atrans, pcamatrix A, bool btrans, pch2matrix B, pamatrix C)
	Matrix multiplication $C \gets C + \alpha A B$ , $C \gets C + \alpha A^* B$ , $C \gets C + \alpha A B^$ or $C \gets C + \alpha A^ B^*$ . More...

void	collectdense_h2matrix (pcamatrix a, pcclusterbasis rb, pcclusterbasis cb, pamatrix s)
	Compute $S \gets V_t^* A W_s$ . More...

void	project_amatrix_h2matrix (ph2matrix h2, pcamatrix a)
	Compute the best approximation of a given matrix with respect to an $\mathcal{H}^2$ -matrix space. More...

void	project_hmatrix_h2matrix (ph2matrix h2, phmatrix h)
	Compute the best approximation of a given matrix with respect to an $\mathcal{H}^2$ -matrix space. More...

real	norm2_h2matrix (pch2matrix H2)
	Approximate the spectral norm $\\|H\\|_2$ of a matrix . More...

real	norm2diff_h2matrix (pch2matrix a, pch2matrix b)
	Approximate the spectral norm $\\|A-B\\|_2$ of the difference of two matrices and . More...

void	write_cdf_h2matrix (pch2matrix G, const char *name)
	Write h2matrix to NetCDF file. More...

void	write_cdfpart_h2matrix (pch2matrix G, int nc_file, const char *prefix)
	Write h2matrix to part of a NetCDF file. More...

ph2matrix	read_cdf_h2matrix (const char *name, pclusterbasis rb, pclusterbasis cb)
	Read h2matrix from NetCDF file. More...

ph2matrix	read_cdfpart_h2matrix (int nc_file, const char *prefix, pclusterbasis rb, pclusterbasis cb)
	Read h2matrix from part of a NetCDF file. More...

void	write_cdfcomplete_h2matrix (pch2matrix G, const char *name)
	Write h2matrix to NetCDF file, including cluster trees and cluster bases. More...

ph2matrix	read_cdfcomplete_h2matrix (const char *name)
	Read h2matrix from NetCDF file, including cluster trees and cluster bases. More...

void	draw_cairo_h2matrix (cairo_t *cr, pch2matrix G, bool storage, uint levels)
	Draw a h2matrix to a cairo surface. More...

uint	getrows_h2matrix (pch2matrix h2)
	Get the number of rows of an h2matrix . More...

uint	getcols_h2matrix (pch2matrix h2)
	Get the number of columns of an h2matrix . More...

Detailed Description

Representation of an $\mathcal{H}^2$ -matrix.

The h2matrix class is used to represent $\mathcal{H}^2$ -matrices with arbitrary block structures and arbitrary cluster bases.

Typedef Documentation

typedef void(* h2matrix_callback_t) (ph2matrix G, uint mname, uint rname, uint cname, uint pardepth, void *data)

Callback function for h2matrix iterators.

Parameters

G	Matrix.
mname	Number of matrix.
rname	Number of row cluster.
cname	Number of column cluster.
pardepth	Parallelization depth.
data	Additional data.

typedef void(* h2matrixlist_callback_t) (pccluster t, uint tname, uint pardepth, pch2matrixlist hl, void *data)

Callback function for h2matrixlist iterators.

Parameters

t	Cluster.
tname	Number of cluster.
pardepth	Parallelization depth.
hl	List of h2matrix objects.
data	Additional data.

Function Documentation

void addeval_h2matrix_avector	(	field	alpha,
		pch2matrix	h2,
		pcavector	x,
		pavector	y
	)

Matrix-vector multiplication $y \gets y + \alpha A x$ .

The matrix is multiplied by the source vector $x$ , the result is scaled by $\alpha$ and added to the target vector $y$ .

Parameters

alpha	Scaling factor $\alpha$ .
h2	Matrix .
x	Source vector .
y	Target vector .

void addevalsymm_h2matrix_avector	(	field	alpha,
		pch2matrix	h2,
		pcavector	x,
		pavector	y
	)

Symmetric matrix-vector multiplication, $y \gets y + \alpha A x$ , where $A$ is assumed to be self-adjoint and only its lower triangular part is used.

Parameters

alpha	Scaling factor $\alpha$ .
h2	Matrix .
x	Source vector .
y	Target vector .

void addevaltrans_h2matrix_avector	(	field	alpha,
		pch2matrix	h2,
		pcavector	x,
		pavector	y
	)

Adjoint matrix-vector multiplication $y \gets y + \alpha A^* x$ .

The adjoint matrix is multiplied by the source vector $x$ , the result is scaled by $\alpha$ and added to the target vector $y$ .

Parameters

alpha	Scaling factor $\alpha$ .
h2	Matrix .
x	Source vector .
y	Target vector .

void addmul_amatrix_h2matrix_amatrix	(	field	alpha,
		bool	atrans,
		pcamatrix	A,
		bool	btrans,
		pch2matrix	B,
		pamatrix	C
	)

Matrix multiplication $C \gets C + \alpha A B$ , $C \gets C + \alpha A^* B$ , $C \gets C + \alpha A B^*$ or $C \gets C + \alpha A^* B^*$ .

Multiplies an amatrix by an h2matrix. For the truncated multiplication of two h2matrix objects, see addmul_h2matrix.

Parameters

alpha	Scaling factor $\alpha$ .
atrans	Set if is to be used instead of .
A	First source amatrix .
btrans	Set if is to be used instead of .
B	Second source h2matrix .
C	Target amatrix .

void addmul_h2matrix_amatrix_amatrix	(	field	alpha,
		bool	atrans,
		pch2matrix	A,
		bool	btrans,
		pcamatrix	B,
		pamatrix	C
	)

Matrix multiplication $C \gets C + \alpha A B$ , $C \gets C + \alpha A^* B$ , $C \gets C + \alpha A B^*$ or $C \gets C + \alpha A^* B^*$ .

Multiplies an h2matrix by an amatrix. For the truncated multiplication of two h2matrix objects, see addmul_h2matrix.

Parameters

alpha	Scaling factor $\alpha$ .
atrans	Set if is to be used instead of .
A	First source h2matrix .
btrans	Set if is to be used instead of .
B	Second source amatrix .
C	Target amatrix .

ph2matrix build_from_block_h2matrix	(	pcblock	b,
		pclusterbasis	rb,
		pclusterbasis	cb
	)

Build an h2matrix object from a block tree using given cluster bases.

Remarks: Submatrices for far- and nearfield leaves are created, but their coefficients are not initialized.

Parameters

b	Block tree.
rb	Row cluster basis.
cb	Column cluster basis.

Returns: New h2matrix object.

pblock build_from_h2matrix_block ( pch2matrix G )

Build an block tree from an h2matrix.

Parameters

G	Input h2matrix.

Returns: New block tree corresponding to the structure of G.

void clear_h2matrix ( ph2matrix h2 )

Set an h2matrix to zero by clearing all far- and nearfield matrices.

Parameters

h2	Target matrix.

ph2matrix clone_h2matrix	(	pch2matrix	h2,
		pclusterbasis	rb,
		pclusterbasis	cb
	)

Builds a new h2matrix with clusterbasis rb and cb and the block structure of h2. Copies all coupling matrices $S_b,\ b \in \mathcal L_{\mathcal I \times \mathcal J}^+$ to the clone.

Parameters

h2	Input h2matrix which has to be cloned.
rb	Row clusterbasis for the clone.
cb	Column clusterbasis for the clone.

Returns: New h2matrix with clusterbasis rb and cb and the same data as h2.

ph2matrix clonestructure_h2matrix	(	pch2matrix	h2,
		pclusterbasis	rb,
		pclusterbasis	cb
	)

Builds a new h2matrix with clusterbasis rb and cb and the block structure of h2.

Parameters

h2	Input h2matrix whose structure has to be cloned.
rb	Row clusterbasis for the clone.
cb	Column clusterbasis for the clone.

Returns: New h2matrix with clusterbasis rb and cb and the same block structure as h2.

void collectdense_h2matrix	(	pcamatrix	a,
		pcclusterbasis	rb,
		pcclusterbasis	cb,
		pamatrix	s
	)

Compute $S \gets V_t^* A W_s$ .

If row and column basis are orthogonal, the result is the coupling matrix for the optimal approximation of $A$ in these bases with respect to the spectral and Frobenius norms.

Parameters

a	Source matrix .
rb	Row basis $(V_t)_{t\in{\mathcal T}_{\mathcal I}}$ .
cb	Column basis $(W_s)_{s\in{\mathcal T}_{\mathcal J}}$ .
s	Target matrix, will be overwritten by .

void del_h2matrix ( ph2matrix h2 )

Delete an h2matrix object.

Releases the storage corresponding to the object. If this h2matrix contains pointers to submatrices, the submatrices are released by unref_h2matrix.

Only objects with h2->refs==0 may be deleted.

Parameters

h2	Object to be deleted.

void draw_cairo_h2matrix	(	cairo_t *	cr,
		pch2matrix	G,
		bool	storage,
		uint	levels
	)

Draw a h2matrix to a cairo surface.

Parameters

cr	Cairo surface to be drawn to.
G	The h2matrix that should be drawn.
storage	Flag that indicates if the storage requirements for every block should be depicted into the graphic.
levels	Number of levels of the h2matrix that should be drawn. If `level` == 0 holds, all levels will be drawn.

ph2matrix* enumerate_h2matrix ( ph2matrix h2 )

Enumerate h2matrix according to block tree.

The h2matrix submatrices are enumerated in an array of size h2->desc. The enumeration starts with 0 assigned to the root and then proceeds column-wise starting with b->sons[0] corresponding to the entries 1 to h2->sons[0]->desc in the array and ending with h2->sons[rsons*csons-1] corresponding to the last b->sons[rsons*csons-1]->desc entries.

Parameters

h2	Matrix matching the block structure given by `b`.

Returns: Array of size h2->desc containing pointers to the h2matrix objects corresponding to descendants of h2.

void fastaddeval_h2matrix_avector	(	field	alpha,
		pch2matrix	h2,
		pavector	xt,
		pavector	yt
	)

Interaction phase of the matrix-vector multiplication.

Nearfield blocks are added directly $y|_{\hat t} \gets y|_{\hat t} + A|_{\hat t\times\hat s} x|_{\hat s}$ , farfield block contributions are accumulated $\hat y_t \gets \hat y_t + S_{t,s} \hat x_s$ .

Both xt and yt should be coefficient vectors provided by new_coeffs_clusterbasis_avector, xt is usually initialized by forward_clusterbasis_avector, while yt is typically added to the result using backward_clusterbasis_avector.

Parameters

alpha	Scaling factor $\alpha$ .
h2	Matrix .
xt	Coefficients $(\hat x_s)_{s\in\mathcal{T}_{\mathcal J}}$ of the source vector with respect to the column basis `h2->cb`.
yt	Coefficients $(\hat y_t)_{t\in\mathcal{T}_{\mathcal I}}$ of the target vector with respect to the row basis `h2->rb`.

void fastaddevaltrans_h2matrix_avector	(	field	alpha,
		pch2matrix	h2,
		pavector	xt,
		pavector	yt
	)

Interaction phase of the adjoint matrix-vector multiplication.

Nearfield blocks are added directly $y|_{\hat s} \gets y|_{\hat s} + A|_{\hat t\times\hat s}^* x|_{\hat t}$ , farfield block contributions are accumulated $\hat y_s \gets \hat y_s + S_{t,s}^* \hat x_t$ .

Both xt and yt should be coefficient vectors provided by new_coeffs_clusterbasis_avector, xt is usually initialized by forward_clusterbasis_avector, while yt is typically added to the result using backward_clusterbasis_avector.

Parameters

alpha	Scaling factor $\alpha$ .
h2	Matrix .
xt	Coefficients $(\hat x_t)_{t\in\mathcal{T}_{\mathcal I}}$ of the source vector with respect to the row basis `h2->rb`.
yt	Coefficients $(\hat y_s)_{s\in\mathcal{T}_{\mathcal J}}$ of the target vector with respect to the column basis `h2->cb`.

void fastaddmul_h2matrix_amatrix_amatrix	(	field	alpha,
		bool	atrans,
		pch2matrix	A,
		pcamatrix	Bt,
		pamatrix	Ct
	)

Interaction phase of the h2matrix - amatrix multiplication.

If atrans==false, nearfield blocks are added directly $C|_{\hat t\times m} \gets C|_{\hat t\times m} + \alpha A|_{\hat t\times\hat s} B|_{\hat s\times m}$ , farfield block contributions are accumulated $\widehat Y_t \gets \widehat Y_t + \alpha S_{t,s} \widehat B_s$ . Both bt and ct should be coefficient matrices with the same number of columns and cb->ktree and rb->ktree rows, respectively.

If atrans==true, nearfield blocks are treated by $C|_{\hat s\times m} \gets C|_{\hat s\times m} + \alpha A|_{\hat t\times\hat s}^* B|_{\hat t\times m}$ , farfield block contributions are accumulated $\widehat Y_s \gets \widehat Y_s + \alpha S_{t,s}^* \widehat B_t$ . Both bt and ct should be coefficient matrices with the same number of columns and rb->ktree and cb->ktree rows, respectively.

bt is usually initialized by forward_clusterbasis_amatrix, while ct is typically added to the result using backward_clusterbasis_amatrix.

Parameters

alpha	Scaling factor $\alpha$ .
atrans	Set if is to be used instead of .
A	First source matrix .
Bt	Second source matrix, expressed through coefficient matrices $(\widehat X_s)_{s\in\mathcal{T}_{\mathcal J}}$ of the second source matrix with respect to the column basis `h2->cb` if `atrans==false` and through $(\widehat X_t)_{t\in\mathcal{T}_{\mathcal I}}$ with respect to the row basis `h2->rb` otherwise.
Ct	Target matrix, expressed through coefficient matrices $(\widehat Y_t)_{t\in\mathcal{T}_{\mathcal I}}$ with respect to the row basis `h2->rb` if `atrans==false` and through $(\widehat Y_s)_{s\in\mathcal{T}_{\mathcal J}}$ with respect to the column basis `h2->cb` otherwise.

uint getcols_h2matrix ( pch2matrix h2 )

Get the number of columns of an h2matrix $G$ .

Parameters

h2 Matrix .

Returns: Number of columns of .

size_t getfarsize_h2matrix ( pch2matrix h2 )

Get size of the farfield part of a given h2matrix object.

Parameters

h2	$\mathcal{H}^2$ -matrix object.

Returns: Size of allocated storage for farfield in bytes.

size_t getnearsize_h2matrix ( pch2matrix h2 )

Get size of the nearfield part of a given h2matrix object.

Parameters

h2	$\mathcal{H}^2$ -matrix object.

Returns: Size of allocated storage for nearfield in bytes.

uint getrows_h2matrix ( pch2matrix h2 )

Get the number of rows of an h2matrix $G$ .

Parameters

h2 Matrix .

Returns: Number of rows of .

size_t getsize_h2matrix ( pch2matrix h2 )

Get size of a given h2matrix object.

Parameters

h2	$\mathcal{H}^2$ -matrix object.

Returns: Size of allocated storage in bytes.

size_t gettotalsize_h2matrix ( pch2matrix h2 )

Get total size of a given h2matrix object, including cluster bases.

Parameters

h2	$\mathcal{H}^2$ -matrix object.

Returns: Size of allocated storage in bytes.

void iterate_bycol_h2matrix	(	ph2matrix	G,
		uint	mname,
		uint	rname,
		uint	cname,
		uint	pardepth,
		h2matrix_callback_t	pre,
		h2matrix_callback_t	post,
		void *	data
	)

Iterate through all submatrices of an h2matrix.

If the iterator works with multiple threads, it guarantees that threads running in parallel call the pre and post functions with different column clusters.

Parameters

G	Matrix.
mname	Number of matrix block.
rname	Number of row cluster.
cname	Number of column cluster.
pardepth	Parallization depth.
pre	Function called before accessing sons.
post	Function called after accessing sons.
data	Additional data passed to callback functions.

void iterate_byrow_h2matrix	(	ph2matrix	G,
		uint	mname,
		uint	rname,
		uint	cname,
		uint	pardepth,
		h2matrix_callback_t	pre,
		h2matrix_callback_t	post,
		void *	data
	)

Iterate through all submatrices of an h2matrix.

If the iterator works with multiple threads, it guarantees that threads running in parallel call the pre and post functions with different row clusters.

Parameters

G	Matrix.
mname	Number of matrix block.
rname	Number of row cluster.
cname	Number of column cluster.
pardepth	Parallization depth.
pre	Function called before accessing sons.
post	Function called after accessing sons.
data	Additional data passed to callback functions.

void iterate_collist_h2matrix	(	ph2matrix	G,
		uint	mname,
		uint	rname,
		uint	cname,
		uint	pardepth,
		h2matrixlist_callback_t	pre,
		h2matrixlist_callback_t	post,
		void *	data
	)

Iterate through all submatrices of an h2matrix, collecting all column blocks in an h2matrixlist object.

Parameters

G	Matrix.
mname	Number of matrix block.
rname	Number of row cluster.
cname	Number of column cluster.
pardepth	Parallization depth.
pre	Function called before accessing sons.
post	Function called after accessing sons.
data	Additional data passed to callback functions.

void iterate_h2matrix	(	ph2matrix	G,
		uint	mname,
		uint	rname,
		uint	cname,
		uint	pardepth,
		h2matrix_callback_t	pre,
		h2matrix_callback_t	post,
		void *	data
	)

Iterate through all submatrices of an h2matrix.

If the iterator works with multiple threads, it guarantees that threads running in parallel call the pre and post functions with different row and column clusters.

Parameters

G	Matrix.
mname	Number of matrix block.
rname	Number of row cluster.
cname	Number of column cluster.
pardepth	Parallization depth.
pre	Function called before accessing sons.
post	Function called after accessing sons.
data	Additional data passed to callback functions.

void iterate_rowlist_h2matrix	(	ph2matrix	G,
		uint	mname,
		uint	rname,
		uint	cname,
		uint	pardepth,
		h2matrixlist_callback_t	pre,
		h2matrixlist_callback_t	post,
		void *	data
	)

Iterate through all submatrices of an h2matrix, collecting all row blocks in an h2matrixlist object.

Parameters

G	Matrix.
mname	Number of matrix block.
rname	Number of row cluster.
cname	Number of column cluster.
pardepth	Parallization depth.
pre	Function called before accessing sons.
post	Function called after accessing sons.
data	Additional data passed to callback functions.

void mvm_h2matrix_avector	(	field	alpha,
		bool	h2trans,
		pch2matrix	h2,
		pcavector	x,
		pavector	y
	)

Matrix-vector multiplication $y \gets y + \alpha A x$ or $y \gets y + \alpha A^* x$ .

The matrix or its adjoint is multiplied by the source vector $x$ , the result is scaled by $\alpha$ and added to the target vector $y$ .

Parameters

alpha	Scaling factor $\alpha$ .
h2trans	Set if is to be used instead of .
h2	Matrix .
x	Source vector .
y	Target vector .

ph2matrix new_full_h2matrix	(	pclusterbasis	rb,
		pclusterbasis	cb
	)

Create a new h2matrix object representing a standard dense matrix.

Allocates storage for the object containing an amatrix object.

Remarks: Should always be matched by a call to del_h2matrix. This call happens automatically if the last object referencing this object (see ref_h2matrix) is deleted.

Parameters

rb	Row cluster basis.
cb	Column cluster basis.

Returns: New h2matrix object containing a new amatrix.

ph2matrix new_h2matrix	(	pclusterbasis	rb,
		pclusterbasis	cb
	)

Create a new h2matrix object.

Allocates storage for the object and sets the matrix pointers to NULL, representing a zero matrix.

Remarks: Should always be matched by a call to del_h2matrix. This call happens automatically if the last object referencing this object (see ref_h2matrix) is deleted.

Parameters

rb	Row cluster basis.
cb	Column cluster basis.

Returns: New h2matrix object.

ph2matrix new_super_h2matrix	(	pclusterbasis	rb,
		pclusterbasis	cb,
		uint	rsons,
		uint	csons
	)

Create a new hmatrix object representing a subdivided matrix.

Allocates storage for the object representing a matrix with submatrices. The submatrices are initialized with NULL pointers and have to be set up with ref_hmatrix.

Remarks: Should always be matched by a call to del_h2matrix. This call happens automatically if the last object referencing this object (see ref_h2matrix) is deleted.

Parameters

rb	Row cluster basis.
cb	Column cluster basis.
rsons	Number of block rows.
csons	Number of block columns.

Returns: New h2matrix object with submatrices.

ph2matrix new_uniform_h2matrix	(	pclusterbasis	rb,
		pclusterbasis	cb
	)

Create a new h2matrix object representing a uniform matrix.

Allocates storage for the object containing a uniform object.

Remarks: Should always be matched by a call to del_h2matrix. This call happens automatically if the last object referencing this object (see ref_h2matrix) is deleted.

Parameters

rb	Row cluster basis.
cb	Column cluster basis.

Returns: New h2matrix object containing a new uniform matrix.

ph2matrix new_zero_h2matrix	(	pclusterbasis	rb,
		pclusterbasis	cb
	)

Create a new h2matrix object representing a zero matrix.

Allocates storage for the object representing a zero matrix.

Remarks: Should always be matched by a call to del_h2matrix. This call happens automatically if the last object referencing this object (see ref_h2matrix) is deleted.

Parameters

rb	Row cluster basis.
cb	Column cluster basis.

Returns: New h2matrix object.

real norm2_h2matrix ( pch2matrix H2 )

Approximate the spectral norm $\|H\|_2$ of a matrix $H$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $H^* H$ and computing the square root of the resulting eigenvalue approximation.

Parameters

H2	$\mathcal H^2$ matrix .

Returns: Approximation of $\|H\|_2$ .

real norm2diff_h2matrix	(	pch2matrix	a,
		pch2matrix	b
	)

Approximate the spectral norm $\|A-B\|_2$ of the difference of two matrices $A$ and $B$ .

The spectral norm is approximated by applying a few steps of the power iteration to the matrix $(A-B)^* (A-B)$ and computing the square root of the resulting eigenvalue approximation.

Parameters

a	$\mathcal H^2$ matrix .
b	$\mathcal H^2$ matrix .

Returns: Approximation of $\|A-B\|_2$ .

void project_amatrix_h2matrix	(	ph2matrix	h2,
		pcamatrix	a
	)

Compute the best approximation of a given matrix $A$ with respect to an $\mathcal{H}^2$ -matrix space.

All nearfield blocks will be copied (and permuted according to the cluster numbering), all farfield blocks will be approximated by coupling matrices $S_{t,s} = V_t^* A|_{\hat t\times\hat s} W_s$ .

Remarks: In order to obtain the best approximation, both the row basis h2->rb and the column basis h2->cb should be orthogonal.

Parameters

h2	Target matrix, will be overwritten by the best approximation of the source matrix.
a	Source matrix.

void project_hmatrix_h2matrix	(	ph2matrix	h2,
		phmatrix	h
	)

Compute the best approximation of a given matrix $A$ with respect to an $\mathcal{H}^2$ -matrix space.

All nearfield blocks will be copied (and permuted according to the cluster numbering), all farfield blocks $A|_{\hat t\times\hat s} = X Y^*$ will be approximated by coupling matrices $S_{t,s} = (V_t^* X) (W_s^* Y)^*$ .

Remarks: In order to obtain the best approximation, both the row basis h2->rb and the column basis h2->cb should be orthogonal.

Parameters

h2	Target matrix, will be overwritten by the best approximation of the source matrix.
h	Source matrix.

void random_h2matrix ( ph2matrix h2 )

Fill an h2matrix with random coefficients.

Parameters

h2	Target matrix .

ph2matrix read_cdf_h2matrix	(	const char *	name,
		pclusterbasis	rb,
		pclusterbasis	cb
	)

Read h2matrix from NetCDF file.

Parameters

name	File name.
rb	Row cluster basis.
cb	Column cluster basis.

Returns: h2matrix read from file.

ph2matrix read_cdfcomplete_h2matrix ( const char * name )

Read h2matrix from NetCDF file, including cluster trees and cluster bases.

Parameters

name	File name.

Returns: h2matrix read from file.

ph2matrix read_cdfpart_h2matrix	(	int	nc_file,
		const char *	prefix,
		pclusterbasis	rb,
		pclusterbasis	cb
	)

Read h2matrix from part of a NetCDF file.

Parameters

nc_file	File handle.
prefix	Prefix for variable names.
rb	Row cluster basis.
cb	Column cluster basis.

Returns: h2matrix read from file.

void ref_h2matrix	(	ph2matrix *	ptr,
		ph2matrix	h2
	)

Set a pointer to an h2matrix object, increase its reference counter, and decrease reference counter of original pointer target.

Parameters

ptr	Pointer to the ph2matrix variable that will be changed.
h2	h2matrix that will be referenced.

void scale_h2matrix	(	field	alpha,
		ph2matrix	h2
	)

Scale an h2matrix by a factor.

Parameters

alpha	Scaling factor $\alpha$ .
h2	Target matrix , will be overwritten by $\alpha G$ .

void unref_h2matrix ( ph2matrix h2 )

Reduce the reference counter of an h2matrix object.

If the reference counter reaches zero, the object is deleted.

Remarks: Use ref_h2matrix with h2=NULL instead, since this guarantees that the pointer is properly invalidated.

Parameters

h2	h2matrix that will be unreferenced.

void update_h2matrix ( ph2matrix h2 )

Complete the initialisation of a h2matrix object.

Complete the initialisation of the h2matrix object after all sons have been initialised. The number of the descendants of the $\mathcal{H}^2$ -matrix is computed from the desc fields of its sons.

Parameters

h2	$\mathcal{H}^2$ -matrix to be completed.

void write_cdf_h2matrix	(	pch2matrix	G,
		const char *	name
	)

Write h2matrix to NetCDF file.

Parameters

G	Matrix.
name	File name.

void write_cdfcomplete_h2matrix	(	pch2matrix	G,
		const char *	name
	)

Write h2matrix to NetCDF file, including cluster trees and cluster bases.

Parameters

G	Matrix.
name	File name.

void write_cdfpart_h2matrix	(	pch2matrix	G,
		int	nc_file,
		const char *	prefix
	)

Write h2matrix to part of a NetCDF file.

Parameters

G	Matrix.
nc_file	File handle.
prefix	Prefix for variable names.

Data Structures

Typedefs

Functions

Detailed Description

Typedef Documentation

Function Documentation